Grinding mill



Dec. 28, 1965 YUKIO MATSUBAYASHI ETAL 3,225,044

GRINDING MILL Filed Oct. 24, 1962 2 Sheets-Sheet 1 Dec. 28, 1965 YUKlOMATSUBAYASHI ETAL 3,226,044

GRINDING MILL 2 SheetsSheet 2 Filed Oct. 24, 1962 United States Patent f3,226,044 GRINDING MILL Yukio Matsubayashi and Ryokichi Sato, Ichikawa,Chibaken, Japan, assignors to Nisso Seiko Kabushiki Kaisha, Tokyo,Japan, a corporation of Japan Filed Oct. 24, 1962, Ser. No. 233,501Claims priority, application Japan, Oct. 27, 1961, 36/315,517,36/38,518, 36/326,519, 36/38,520 8 Claims. (Cl. 241-172) The presentinvention relates to a continuous fine grinding mill and a method ofgrinding by this mill. It is well known to suspend a screw in acylindrical shell, pack grinding media into the space between the shelland the screw and grind the material which is suspended in fluid, forexample water or air, by abrasive action caused by rotating the screw.But in such a device the grinding media is always moved upward, downwardand round repeatedly, which results in a severe contact of the grindingmedia or the material to be ground with the shell or the screw. Coatingof wear-resistant materials such as rubber in order to prevent abrasionby said severe contact is already known. But rubber-coating is veryexpensive and if once a part of the coating is broken, this breakageextends without delay to other parts, which results in an exfoliation ofthe coating and therefore in a considerable decrease of the durableyears of the device.

The inventors of this application have theoretically analyzed motions ofgrinding media within a grinding mill according to soil mechanics andfound that said drawback is due to unreasonable motions of grindingmedia within the mill shell. Grinding action of this kind is namelyeffected in such manner that all of the individual of media make contactmotions with one another under a packed condition and cause abrasions ofmaterial particles at contact points of the individuals. Therefore, theideal grinding conditions should be such that voids of packed media arealways filled up with suspension of material particles in a high densityand the individuals of media make motions under a perfectly packedcondition, that is to say, the individuals of media contact with eachother in such a manner that the surface of each medium is covered wtihmaterial particles. Under the above conditions in which the wear ofmedia can be remarkably minimized, the abrasion of material particlesbecomes predominant and a greater part of power consumed in the motionsof media can be efficiently utilized in abrasing the material, a millcan perform much more effective fine grinding than a ball mill and soon. In this connection, the inventors have found that the grinding mediacan reasonably be removed and circulated in such fashion that they areconveyed upward through a spiral flowing path within the screw and moveddownward through a vertical flowing path located around the screw undera perfectly packed condition by regulating packed volume of media, speedof rotation of the screw and pitch thereof.

In order that the invention may be more readily understood, oneembodiment will now be described with reference to the accompanyingdrawings, in which:

FIG. 1 is a vertical side-section of a preferred embodiment of a finegrinding mill according to the invention,

FIGS. 2-5 are schematic drawings illustrating undesirable movements ofgrinding media in a tower mill.

In the grinding mill illustrated in FIG. 1, a screw 3,226,044 PatentedDec. 28, 1965 formed with spiral wings 2a is suspended in a cylindricalshell 1. The inner space of the mill is packed up to a height which islocated higher than the top end of the screw with grinding media such asiron balls, steel balls, corundum balls, etc., and granular or massivematerials. When the screw 2 is rotated by a driving device provided witha continuous speed-controller, grinding media are conveyed upward bypushing up action of the screw and then moved downward, which isrepeated continuously. According to the inventors study, grinding mediacan be conveyed upward through the spiral flowing path within the screwand moved downward through the vertical ring-shaped flowing path locatedaround the screw keeping a perfectly packed condition by regulating thedimensions and the operation conditions of the present device. But inthis case the grinding media fall plumb down or effect circular motionsalong the internal surface of the shell, whereby this internal surfaceis subject to a serious rubbing with said media. According to thepresent invention, several circular horizontal ribs 3 and vertical ribs4 are fixed on the internal surface of the shell and thereby a staticlayer of media is made along the internal surface even while thegrinding media move within the shell. It results therefrom that thedirect rubbing between the internal surface of the shell and thegrinding media comes to a standstill and the internal surface can beperfectly free from wearing, so that the power consumed in said rubbingaction can be converted to effective abrasing energy. The mutualdistances between the ribs depend on dimension and shape of the shelland the screw and the size of the grinding media. The ribs can be soarranged that its direction is somewhat inclined and the width of ribsin general should be two or three times the size of media. According tothe invention it is not necessary for the internal surface of the shellto be made of or coated with special wear-resistant materials. Ifnecessary, the coating can be done only on the edge of ribs in order toimprove considerably the durability thereof. The construction of thescrew will be then illustrated as follows: i

As shown in FIG. 1, the screw has a special bottom construction whichconsists of a disc 14 fixed on the bottom of the screw 2 and radial ribs5 fixed on the back of the disc 14. The radial ribs are fixed in such away that the edges of them form geometrical generating lines of aconical surface. The bottom construction serves to prevent the localwear of the screw-end and due to this construction even the ends of thescrew wings 2a serve to convey the grinding media.

When a screw without said bottom construction is rotated in the mill,the end-edges of spiral surfaces of the screw have to push through thepacked bed of media against high grain pressure of packed media, andalso severe rubbing action inevitably occurs between the backend-surfaces and the end-edges of spiral surfaces of the screw wings andthe packed media. These phenomena result in an extremely rapid wear ofthe screw-end. The disc serves to prevent such a direct rubbing actionand further for the purpose that also the end of the spiral surfaces ofthe screw wings causes the grinding media to effect the same soilmechanical motion as the upper spiral surfaces of the screw wings. Byfixing only a disc at the end of a screw a direct rubbing action on theback plane of the disc with materials is unavoidable, which results in arapid wear of the disc. Radial ribs should be fixed to prevent the wearof back surface of the disc as they hold grinding media between the ribsand when the screw is rotated mutual friction of media occur on theinverted conical surface. In addition, material particles are forced tomove toward outside of the conical surface by means of centrifugalforce, thus the bottom construction serves to prevent the wear of thedisc by material particles. In this case the abrasion of the disc occurson its edge as well as that of the screw-wings and thereby thedurability of the disc and the screw-wings become same. However, it isundoubtedly unavailable energy having no relation to the motion of mediaor grinding action that is consumed for rotating the inverted coneagainst friction force acting on the conical surface. This unavailableenergy consumption can be decreased up to 58% of the total consumedenergy by adopting a considerably high value of the ratio of the motionheight of media to the effective diameter of the shell. One way toeliminate said unavailable energy is to arrange a bearing at the lowerend of the screw, but the bearing in this case cannot be endurable for asevere wear. According to the abovementioned reasonable designcondition, only a vertical force exerts on the screw shaft and thereforeno lateral oscillation occurs, so that a lower bearing is not required.

Various screws for this invention can be formed. For example, a screwcan be provided with screw-wings having a small diameter in order tomaintain a high strength, the spiral surfaces of the screw beingdesirably divided into small and replaceable wing-pieces which have aprescribed radius and are made of wear-resistant material such aschilled cast iron, heat-treated special steel, tile, etc.

The enlarged part 6 of the shell 1 is provided for the purpose ofpreventing local wear of the disc 14 which would be caused by rapid flowof the suspension having material particles suspended due to the factthat the vertical flowing cross-sectional area around the screw isreduced by the disc. According to the invention, the relation betweentheeffective inside diameters D D of the shell and the enlarged partthereof and the diameters d d of the screw-wings and the screw shaftshould be chosen as follows:

net/m The bottom of said enlarged part of the shell has an invertedcone-like construction as shown in FIG. 1. The angle of inclination ofthe inverted conical surface should be a little larger than the angle ofrepose of material particles to prevent precipitation of theseparticles. Media located under the disc, formingaicompletely staticpacked column and having no relation to grinding action, can besubstituted for other substances. In selecting the substances, it isonly necessary that static packed columns of them have high fractionalvoid volumes and have enough strength to support load of the packedcolumn of moving media. This packed column can be supported by a gridplate through which the material particles can pass. In addition thedisc of the screw can be supported directly from below by a slidemechanism, which is so arranged that the material cannot enter saidslide mechanisms by forcing high pressure fluid into said mechanisms.The suspension of material particles so small as to pass freely throughvoids of packed column of media is fed into the shell from above, flowsdown through the shell to the lower outlet 7 and is conveyed circularlyby a pump 12 from the outlet to the upper part of the shell. The newlysupplied material and fluid enter the classification device 8, 11through a flow-in funnel 10 together with the circulated suspension. Inthe classification vessel 8, the fine particles which require no furthergrinding are suspended in the upward current of fluid caused bycontinuous flowing-in of the fluid, and are overflowed from the wholeedge of the vessel 8 into the flow-out through 9. 11 denotes thesize-controller, which can be raised and lowered automatically or byhand by an elevating mechanism 13.

Sectional area for classifying action being reduced by lowering theposition of 13, the overflowing speed becomes larger and thereforecoarser particles can be overflowed, while being enlarged by raising it,finer particles are overflowed. By thus controlling the position of thesize-controller, the fixed size of ground product can be attained alsoin case of fluctuations of feed quantity or the size of ground productcan be controlled. In addition, construction of the shell, flowingsystem of suspend and classification means can be subject to somemodifications. For example, the internal surface of the shell can beprovided with coating of rubber, the suspension can be flowed out fromthe circumference of the enlarged part of the shell, the classificationdevice can be arranged separately or the suspension of the materialparticles and the circulated fluid can be conveyed upward to the upperpart of the packed column through pipes extended along the shell wall.Further, in case of preventing iron oxide from mixing in ground productor in case of using corrosive fluid grinding media containing no ironshould be used and (or) the internal surface of the shell and the outersurface of the screw should be coated with plastics and so on. In caseof using gas as suspension cyclone and the ke can be used asclassification device.

The constructional characteristics of the grinding mill according to thepresent invention have stated above and the determination of the maindimensions and the operational method of said grinding mill will beexplained as follows:

In the embodiment of this invention shown in FIG. 1 the screw should beregarded as a screw conveyor with diameter d When the screw is rotatedto the arrow direction in FIG. 1 by a driving device provided with acontinuous speed-controller, grinding media are conveyed upward withinthe screw and then moved downward between the shell and the screw, thusdoing a circular motion upward and downward, and in this case the heightof packed column has a great influence on the motion of the grindingmedia. For example, when the packed grinding media are too little inquantity and the upper end of the packed layer has the same level asthat of the screwwin-gs, as is shown in FIG. 2, the first one pitch ofthe screw cannot serve to convey up media and the media here cannot butslide down to the outside of Li -cylinder, which results in a local wearof the first one pitch of the screw. In FIGS. 2-5 the hatching partsshow static medium layers and the arrow directions the motionaldirections of the grinding media. Moreover, as said pitch of the screwcannot serve to convey up media, the grinding capacity of the millcannot be fully applied.

The grinding mill according to the invention is packed with media up tothe total height H which consists of the effective length of the screwand the height H as shown in FIG. 1, when H is called height of theadditional packed bed of media. When the mill is packed with mediabeyond the fixed height H motion of grinding media in the height Hbecomes more and more inactive with increasing the height, until themovement of media located in the height H, comes to a stop as shown inFIG. 3. Under such a condition, the edges of upper end of the screw aredirectly rubbed by the static media layer and their rapid wear occurs.In addition, the grinding media located in the height H cannot serve togrind the material. The inventors have found that the height of theadditional packed bed of media H can be obtained from the followingformula:

D (i 4H 1f tan g0 11' (,0 0 tan eo'- 2 tanz Z where D d double distancebetween the ribs of the shell and the screw-wings angle of internalfriction of media K: earth pressure coefficient for a vertical breaksurface When thus a suitable additional packed bed of media is formedaccording to the invention, the grinding media located in d -cylinderare subject to a horizontal packing-pressure from the outer side of d-cylinder and thereby soil-mechanical break surfaces occur in the mediumlayer between the screw-wings, the media in (l -cylinder are conveyedupward in a definite angle in which a slip occurs most easily. Inaddition, the grinding media located above the screw-surfaces are in thesame active motion as that within the screw and also above thescrew-wings the media are conveyed upward, which results in the samewear of the first one pitch as that of the other pitches of the screw.The additional packed bed of media serves to increase medium-pressure inthe mill. Thus the whole length of the screw contributes to conveyingaction of media and the local wear of the screw-end is completelyprevented.

Further, the motion of the grinding media is closely related with thespeed of rotation of the screw. When the screw is rotating, centrifugalforce acting on each individual particle of media in the d -cylindergenerates a horizontal medium-pressure which acts outward on the innersurface of d -cylinder. This centrifugal mediumpressure is balanced tothe external medium-pressure which acts inward on the outer surface of d-cylinder. In the higher level of the packed column a pot-shaped cavityis formed around the screw shaft as shown in FIGS. 2, 4 and 5, becausethe external medium-pressure is lower. A cavity in which materialparticles are only passing by serves nothing for grinding action and itsformation is nothing but consuming unavailable power and causes also thewear of the screw-wings. However, so long as the screw is rotated, theformation of a cavity is unavoidable so that it is desirable to restrictthe cavity formation within the additional packed layer with the heightH For this purpose, the angular velocity w (rod/sec.) of the screwshould be chosen as follows:

d diameter of the screw-wings d diameter of the screw shaft D eifectiveinner diameter of the shell Further, according to the inventors studiesthe screwpitch has an influence upon the motion of the grinding media.

In case of a suitable pitch dire-ct contacts of media with the wingsurfaces of the screw do not occur and the grinding media are pushed upmost easily along break surfaces. If the pitch is too large anunreasonable motion of media is made in the mill as shown in FIG. 5.Considering a bed of media held in any one pitch ab of the screw, thevalue of static medium-pressure must be zero at a and increases toward[2 in proportion to the depth of packed media. Therefore, in the upperpart of the bed, where static medium-pressure is very low, media can bepushed up by external medium-pressure acting on the outer surface of Li-cylinder, in the lower part, sliding action of media is caused byconsiderably high static medium-pressure. In this case, only incompleteconveying action can be done in the mill and the spiral surfaces of thescrew are directly rubbed by sliding media. And as the angle of internalfriction of coarse media is larger in general than that of fine media,the coarse media gather at the upper part of the bed and the fine mediaat the lower part, which results in a decrease of grinding action. Inorder to prevent such a disadvantage, the screw-pitch p must be withinsuch an adequate range given by the following formula:

ir- 2 O+P) tan s v t 2 4p tan (,0 e D d an Thus according to theinvention, the reasonable motion of media can be facilitated or ensuredby satisfying one or all of the conditions for packing height ofgrinding media, speed of rotation of the screw and the screw-pitch andconsequently the durable years of the screw can be considerablylengthened. As under such a motion condition the vertical media layeraround the screw has the highest packing pressure and a part of medialocated between the screw-wings moves outward into said vertical medialayer through the voids of media due to centrifugal force, thescrew-wings are subject to about a uniform wear from their outer-edgesto the inner sides over the total length. In this case the screwsurfaces are free from wearing and hence do not need any coating ofwear-resistant materials over their total length, so only wear at theedge of the screw surfaces must be considered. When the screw-wingssubject to wear and their radii become smaller, the motion of grin-dingmedia would become inactive naturally and the grinding capacity of themill would be reduced. But the mill according to the invention can beoperated under a definite grinding capacity while the wear of thescrew-wings is within an allowable limit, and that in such a manner thatthe speed of rotation of the screw becomes so large with decreasing theradii of the screw-wings by means of the continuous speed-controllerthat the required power for rotating the screw is always kept constant.

Further, to adjust the grinding capacity is important for carrying outthe present invention and also a characteristic thereof. In general thesmallest wear of the grinding media and the greatest grinding capacitycan be obtained only when the highest suspension density of materialparticles exists around the grinding media under the perfectly packedcondition. When the pulp density in the mill is dilute, wear of thegrinding media and waste of power occur due to mutual abrasion of media.In order to prevent such a drawback, the speed of rotation of the screwshould be adjusted so that the density of material particles in thecirculated fluid is kept constant at a maximum allowable value whichstill permits freeflowing of the material particles, by measuring thepulp density. Namely, the grinding capacity should be reduced bydecreasing the speed of rotation of the screw with lowering the pulpdensity and the grinding capacity should be promoted by increasing thespeed of rotation with raising the pulp density, whereby an unavailingwaste of power and wear of the grinding media can be prevented.

Then the flow of material particles in the mill will be mentioned below.

The suspension of such small material particles as to pass freelythrough voids of packed column of media is supplied through theclassification device 11, as shown in FIG. 1, and the liquid level ofthe classification device is always kept constant by overflowing overits total circumference, so that there is no deflection in the suppliedliquid into the shell and its flow-in speed can be easily regulated byadjusting the flowing section of the lower outlet. In addition, thesuspension is supplied into the shell and moved downward therein at sucha velocity that the superficial mean velocity of the suspension based onempty column cross section (namely the velocity when supposing thatthere is no grinding media in the shell and the suspension flowsdownward uniformly) is approximately equal to the settling velocity ofthe grinding media in the concerned static liquid. By selecting such avelocity the material particles circulate through the shell togetherwith the grinding media without being deposited on the grinding medialayer or at the bottom of the shell. When the velocity is too rapid, thematerial particles flow down mainly through the outside of d -cylinder,which results in a lowering of the grinding action of the mill. On theother hand, when said velocity is too late, precipitation of materialparticles is caused mainly at the bottom of the mill, an irregular flowoccurs and the grinding media are pushed up. It results therefrom thatthe lower end of the screw is subject to wearing and, moreover, thegrinding action is lowered. The material particles flows through the 7,voids of the grinding media together with the fluid and, in this case,the direction and the speed of said flow are in accordance with that ofthe motion of the grinding media layer in a regular state. The fluidhaving material particles suspended fills the voids of media in aperfectly packed condition and covers the surface of each medium withsuspended particles. Keeping such a condition the fluid is moved upwardwith the grinding media through the spiral flowing path within the screwand conveyed downward through the vertical ring-shaped flowing patharound the screw, because the flow resistance of viscous pulp is so highin the packed column that the motion of media,'that is, the motion ofvoids causes the carrying action of pulp filling the voids in the samedirection and speed. Thus the material particles are ground by thegrinding media.

According to the invention, the fluid flows out through the outlet 7 dueto its static pressure, as the fluid is moved downward in the shell. Inthis case, the capacity of the pump 12 can be determined so as to letthe pulp flow at a suflicient velocity for preventing sedimentation onlyin considering the difference between the maximum height of the pipesupplying the circulated fluid and the liquid level in theclassification vessel 8, which results in a very small required power ofthe pump.

As is already above-mentioned, the size of ground product can becontrolled by regulating the position of the size-controller. In thiscase, the classification device can be advantageously provided with sucha curved surface that the overflowing sectional area changes lineallydepending on the displacement distance of the size controller. Further,when the inclination of the classification device is so sharp that it islarger than the angle of repose of the material particles and there isno possibility of precipitation of the material particles on the surfaceof the classification device, the internal surface of the classificationdevice can be substituted for the flow-in funnel, which therefore can beomitted.

It is very difficult in general grinding mills to keep ground productalways in a definite size also when the feed rate of material ischanged. But in case of using the classification device constructedaccording to the invention the definite size of ground product caneasily be obtained. When a fixed volume of material and liquid issupplied fixing a position of the classification device, the fixed sizeof ground product is obtained naturally, so long as the speed ofrotation of the screw and the feed ratio of material and fluid arefixed. But coarser particles are overflowed when the supplied volume isincreased, while finer particles are overflowed when the supplied volumeis reduced. When the supplied volume is fixed, the size of groundproduct can be controlled by regulating the sectional area of theoverflowing level which can be performed by displacing theclassification device, as is already above-mentioned.

While the invention has been described in detail with respect to apreferred embodiment, it will be understood by those skilled in the artthat various Changes and modifications may be made without departingfrom the spirit and scope of the invention, and it is intended tocoverall such changes and modifications in the appended claims.

We claim:

1. A grinding mill comprising an outer shell having ribs extendinginwardly about its internal surface a screw mounted for rotation withinsaid shell, grinding media packed tightly into said shell, said grindingmedia being composed of particles sufficiently small to lodge betweensaid ribs and to pass downwardly between said ribs and the outerextremities of said screw.

2. A tower mill comprising a vertical screw having spiral screw wings, ashell surrounding said screw, said shell having various ribs extendinginwardly about its inner surface, a disk mounted horizontally at thelower end of said screw, said disk being of equal diameter to, andforming a termination for, the wings of said screw, and grinding mediapacked tightly within said shell and around said screw and disk, saidgrinding media being composed of particles sufliciently small to lodgebetween said ribs and to pass downwardly between said ribs and the outerextremities of said screw.

3. A tower mill as in claim 2 wherein the lower end of said outer shellflares outwardly in the vicinity of said disk.

4. A tower mill as defined in claim 3 wherein said disk has formed alongits undersurface, ribs whose extremities generate an inverted conedepending from said disk as said disk rotates.

5. Apparatus for grinding material by abrasive action, said apparatuscomprising a vertically suspended screw, an outer shell surrounding saidscrew, said outer shell having horizontal and vertical ribs formed aboutits internal surface, grinding media packed tightly into said shell,said grinding media being composed of particles sufficiently small tolodge between said ribs and to pass downwardly between the innerextremities of said ribs and the outer extremities of said screw, saidgrinding media being packed within said shell and around said screw to aheight above the top of said screw below a height which would besufiicient to prevent upward movement of material within said shell uponrotation of said screw and below a height sufficient to develop a staticlayer of grinding material above said screw said height being determinedby the formula where D d is twice the distance between the ribs of theshell and the screw wings, is the angle of internal friction of themedia within the device, and K is the earth pressure coefiicient for avertical break surface.

'6. Apparatus for grinding material by abrasive action, said apparatuscomprising a vertically suspended screw, an outer shell surrounding saidscrew, said outer shell being provided along its internal surface withhorizontally and vertically extending ribs, grinding media packedtightly into said shell, said grinding media being composed of particlessufficiently small to lodge between said ribs and to pass downwardlybetween the ribs and the outer extremities of said screw, said grindingmaterial being packed tightly into said shell to a height above the topof said screw such that centrifugal action produced by rotation of saidparticles by said screw media is insufficient to produce voids ofgrinding material among the wings of the upper portion of said screw,said height of grinding media above the top of said screw also beinginsufiicient to prevent upward movement of material by rotation of saidscrew and further being insufiicient to develop a static layer ofgrinding material above the screw said height being determined by theformula D0 d2 tan 1r (0 4H,, tan o 6 D ,d tan2 (Z where D d is twice thedistance between the ribs of the shell and the screw wings, 5 is theangle of internal friction of the media within the device, and K is theearth pressure coefiicient for a vertical break surface.

7. Apparatus for grinding material by abrasive action, said apparatuscomprising a vertically suspended screw, an outer shell surrounding saidscrew, said outer shell having horizontal and vertical ribs disposedabout its internal surface, grinding media packed tightly into saidshell, said grinding media being composed of particles sufiicientlysmall to lodge between said ribs and to pass downwardly between theinner extremities of said ribs and the outer extremities of said screw,said screw having wings arranged at a pitch such as to produce completeupward movement of all grinding media among said wingsupon rotation ofsaid screw.

8. A tower mill comprising a vertical screw having spiral wings, a shellsurrounding said screw, said shell having various ribs extendinginwardly about its inner surface, a disk mounted horizontally at thelower end of said screw, said disk being of equal diameter to, andforming a termination for, the wings of said screw, grinding mediapacked tightly within said shell and around said screw and disk, saidgrinding media being composed of particles sufficiently small to lodgebetween said ribs and to pass downwardly between said ribs and the outerex- 10 tremities of said screw, a centrifugal hydraulic classificationdevice mounted above said column of grinding material and means fortransferring particles having passed 10 down between said screw and saidribs up to said hydraulic classification device.

References Cited by the Examiner UNITED STATES PATENTS 2,592,994 4/ 1952Ahlmann 24l172 X 2,595,117 4/1952 Ahlmann 24l-172 2,779,752 1/1957Vining.

FOREIGN PATENTS 489,171 7/ 1938 Great Britain.

ROBERT C. RIORDON, Primary Examiner. I. SPENCER OVERHOLSER, Examiner.

1. A GRINDING MILL COMPRISING AN OUTER SHELL HAVING RIBS EXTENDINGINWARDLY ABOUT ITS INTERNAL SURFACE A SCREW MOUNTED FOR ROTATION WITHINSAID HSELL, GRINDING MEDIA PACKED TIGHTLY INTO SAID SHELL, SAID GRINDINGMEDIA BEING COMPOSED OF PARTICLES SUFFICIENTLY SMALL TO LODGE BETWEENSAID RIBS AND TO PASS DOWNWARDLY BETWEEN SAID RIBS AND THE OUTEREXTREMITIES OF SAID SCREW.